Issue

TROLL model currently compute leaf lifespan with Reich’s allometry (Reich et al. 1991). But we have shown that Reich’s allometry is underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometry underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.

We tested different models starting from complet model Mcomp: \[ {LL_s}_j \sim \mathcal{logN}({\beta_0}*e^{{\beta_1}_s*{LMA_s}_j^{{\beta_3}_s} - {\beta_2}_s*{Nmass_s}_j^{{\beta_4}_s}},\,\sigma)\,\]

\[s=1,...,S_{=4}~, ~~j=1,...,n_s\] \[{\beta_i}_s \sim \mathcal{N}({\beta_i},\,\sigma_i)\,^I, ~~(\beta_i, \sigma, \sigma_i) \sim \mathcal{\Gamma}(0.001,\,0.001)\,^{2I+1}\] We tested models M1 to M9 detailed in following tabs to find the better trade-off between:

1. Complexity (and number of parameters)
2. Convergence
3. Likelihood
4. Prediction quality with Root Mean Square Error (RMSE)

RMSE was computed by fitting a model without a dataset and evaluating it with the same dataset. RMSE in results are mean RMSE for each dataset. Results are shown for each models in eahc model tabs and summarized in Results tab.

LL graph

Figure 1: Leaf mass per area (LMA), leaf nitrogen content (Nmass) and leaflifespan (LL). Leaf mass per area (LMA in \(g.m^{-2}\)), leaf nitrogen content (Nmass, in \(mg.g^-1\)) and leaf lifespan (LL in \(months\)) are taken in GLOPNET dataset from Wright et al. (2004).

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA - {\beta_2}_s*N,\sigma)\,\] Maximum likekihood of 9.0158557 and RMSE of 13.207

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -2.1040528 and RMSE of 14.361

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} - {\beta_2}_s*N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 16.5819461 and RMSE of 291.664

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA - N,\sigma)\,\] Maximum likekihood of 1.8743912 and RMSE of 12.767

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -0.7373547 and RMSE of 14.215

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 5.457475 and RMSE of 12.369

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA,\sigma)\,\] Maximum likekihood of 4.2155493 and RMSE of 14.391

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of -5.4453681 and RMSE of 14.117

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 9.3372588 and RMSE of 16.06

Convergence

Table

Model M1 seemed to have shown the best trade-off between complexity (\(K=6\) parameters), convergence (see tab M1), likelihood, and prediction quality (see table 1). Figure 2 presents model prediction confidence interval and figure 3 compare Reich’s allometry and model M1 predictions with species functional traits used in TROLL. Nevertheless we will test other predictors gathered from TRY database following a model with the same response curve.

Table 1: Models likelihood and prediction quality.RMSE was computed by fitting a model without a dataset and evaluating it with the same dataset. RMSE in results are mean RMSE for each dataset.

\[LL = 14.277*e^{0.007 *LMA -0.411*Nmass }\]

Graphs